The present invention relates to the analysis of circuits generally and more particularly to the distortion analysis of analog and RF (Radio Frequency) circuits by calculating intermodulation products and intercept points.
Second and third order intermodulation intercept points (IP2 and IP3) are critical design specifications for circuit nonlinearity and distortion. A rapid yet accurate method to compute IP2/IP3 is of great importance in complex RF and analog designs. Conventional computer-aided-design solutions for measuring IP2/IP3 are typically based on multi-tone simulations. For a circuit with a DC (Direct Current) operating point such as a LNA (Low Noise Amplifier), a two-tone simulation is performed at two RF input frequencies ω1 and ω2 (usually closely spaced). When the RF power level is low enough, signals at frequencies ω1−ω2 and 2ω1−ω2 are dominated by second and third order nonlinear effects respectively, and higher order contributions are negligible compared to the leading-order terms. Thus, solutions at ω1−ω2 and 2ω1−ω2 can be used as second and third order intermodulation products (IM2 and IM3) to extrapolate intercept points for IP2 and IP3. For a circuit with a periodic time-varying operating point such as a mixer or a switch capacitor filter, a three-tone simulation at ω1, ω2 and the LO (local oscillator) or clock frequency ωc can be conducted and IM3 can be measured at frequency 2ω1−ω2−ωc [8, 13, 3, 4].
Because of the low RF power setting, very high accuracy is typically required in order to obtain reliable intermodulation results. Particularly in three-tone cases, the numerical dynamic range has to accommodate the large LO signal, the small RF signals, and the nonlinear distortions. Furthermore, a multi-tone simulation is generally inefficient for IP2/IP3 measurements because, in addition to IM2 and IM3 harmonics, this approach also resolves other irrelevant frequencies to all nonlinear orders. This additional overhead can be very expensive in large designs with thousands of transistors.
Essentially, IP2/IP3 calculation is a weakly nonlinear problem. It is substantially concerned with only the leading second or third order effects. The fully converged multi-tone solution that contains every order of nonlinearity is generally unnecessary. A more efficient way is to treat both RF inputs as perturbation to the operating point solution and apply 2nd or 3rd order perturbation theory to calculate IM2 or IM3 at the relevant frequency directly. In this way, the dynamic range is reduced to cover just the RF excitations. The most commonly used perturbative method for distortion analysis is the Volterra series [12, 2, 7, 1, 11, 5, 16, 17]. However, this approach requires second and higher order derivatives of nonlinear devices. In the cases of IP2 and IP3, up to 2nd and 3rd order derivatives are needed respectively. This limits the application of Volterra series in many circuit simulations since most device models don't provide derivatives higher than first order. Also, as the order of Volterra series increases, the complexity of tracking the polynomials grows substantially, and the implementation becomes more and more complicated.
Thus, there is a need for improved calculation of intermodulation intercept points and other characteristics of circuit distortion analysis.